Description

The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its $q$-deformations. We discuss the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. The book contains constructions, discussions of notions, statements of main results, and illustrating examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra $\mathfrak{sl}_2$. This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.